LDI de Dos Tramos
7
LINEAS DE INFLUENCIA Longitud de tramo L= 14 m= 0.65 MOMENTO Ra Re Rc -Ra= 2651.03 Re= 2814.36 Rc= 32.67 Tramo 0.00 ≤ x ≤ 0.65 LONGITUD MOMENTO 0.00 0.00 0.07 -0.06 0.13 -0.12 0.20 -0.18 0.26 -0.24 0.33 -0.31 0.39 -0.37 0.46 -0.43 0.52 -0.49 0.59 -0.55 0.65 -0.61 Tramo 0.65 ≤ x ≤ 14 LONGITUD MOMENTO 0.65 -0.61 2.13 -0.53 3.62 -0.44 5.10 -0.36 6.58 -0.28 8.07 -0.21 9.55 -0.15 11.03 -0.09 12.52 -0.04 14.00 0.00 Tramo 14.00 ≤ x ≤ 28 LONGITUD MOMENTO 14.00 0.00 15.40 0.03 16.80 0.05 18.20 0.06 19.60 0.06 21.00 0.06 22.40 0.05 23.80 0.04 25.20 0.03 26.60 0.02 28.00 0.00 m L L m L L 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2 -0.80 -0.60 -0.40 -0.20 0.00 0.20 DIAGRAMA DE MOMENTO DE L.D.I. LONGITUD MOMENTO Rc= L 2 6 Re= 2×L 3 3×m Ra= 5 6 L 2 − 2×L 3 3×m M PI = 1 Re ( RaX− X 3 6 ) M PI = 1 Re ( RaX − X 3 6 +Re×( X −m) ) M PI = 1 Re ( Rc×(2 L−X)− ( 2 L−X) 3 6 )
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Transcript of LDI de Dos Tramos
LINEAS DE INFLUENCIA
Longitud de tramo L= 14m= 0.65
MOMENTO
Ra Re Rc
-Ra= 2651.03 Re= 2814.36 Rc= 32.67
Tramo0.00 ≤ x ≤ 0.65
LONGITUD MOMENTO0.00 0.000.07 -0.060.13 -0.120.20 -0.180.26 -0.240.33 -0.310.39 -0.370.45 -0.430.52 -0.490.59 -0.550.65 -0.61
Tramo0.65 ≤ x ≤ 14
LONGITUD MOMENTO0.65 -0.612.13 -0.533.62 -0.445.10 -0.366.58 -0.288.07 -0.219.55 -0.1511.03 -0.0912.52 -0.0414.00 0.00
Tramo14.00 ≤ x ≤ 28
LONGITUD MOMENTO14.00 0.0015.40 0.0316.80 0.0518.20 0.0619.60 0.0621.00 0.0622.40 0.0523.80 0.0425.20 0.0326.60 0.0228.00 0.00
m
L L
m
L L
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
-0.80
-0.60
-0.40
-0.20
0.00
0.20
DIAGRAMA DE MOMENTO DE L.D.I.
LONGITUD
MO
ME
NT
O
Rc=L2
6
Re=2×L3
3×m
Ra=56L2−2×L
3
3×m
M PI=1Re (RaX− X
3
6 )
M PI=1Re (RaX− X
3
6+Re×(X−m ))
M PI=1Re (Rc×(2 L−X )−
(2L−X )3
6 )
CORTANTE
Ra Me Rc
Ra= 163.33 -Me= 1829.33 Rc= 32.67
Tramo0.00 ≤ x ≤ 0.65
LONGITUD CORTANTE0.00 0.000.07 -0.010.13 -0.010.20 -0.020.26 -0.020.33 -0.030.39 -0.030.45 -0.040.52 -0.050.59 -0.050.65 -0.06
Tramo0.65 ≤ x ≤ 14
LONGITUD CORTANTE0.65 0.942.13 0.813.62 0.685.10 0.566.58 0.448.07 0.339.55 0.2311.03 0.1412.52 0.0614.00 0.00
Tramo14.00 ≤ x ≤ 28
LONGITUD CORTANTE14.00 0.0015.40 -0.0416.80 -0.0718.20 -0.0919.60 -0.1021.00 -0.0922.40 -0.0823.80 -0.0725.20 -0.0526.60 -0.0228.00 0.00
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
m
L L
Me=−23L3
Ra=56L2
Rc=L2
6
V I=1Me (RaX− X
3
6 )
V I=1Me (RaX− X
3
6+Me)
V I=1Me (Rc×(2L−X )−
(2 L−X )3
6 )
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
-0.80
-0.60
-0.40
-0.20
0.00
0.20
DIAGRAMA DE MOMENTO
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
DIAGRAMA DE CORTANTE
DEDUCCIONDE FORMULA DE LINEA DE INFLUENCIA PARA VIGA HIPEESTATICA DE DOS TRAMOS
MOMENTO
DEDUCCION DE FORMULA DE MOMENTO
1) 0.00 ≤ x ≤ m
2) m ≤ x ≤ L
3) L ≤ x ≤ 2L
CORTANTE
DEDUCCION DE FORMULA DE CORTANTE
1) 0.00 ≤ x ≤ m
2) m ≤ x ≤ L
3) L ≤ x ≤ 2L
m
L L
Rc=L2
6
m
L L
Me=−23L3Ra=
56L2 Rc=L
2
6
Re=2×L3
3×mRa=5
6L2−2×L
3
3×m
M PI=1Re (RaX− X
3
6 )
M PI=1Re (RaX− X
3
6+Re×(X−m ))
M PI=1Re (Rc×(2 L−X )−
(2L−X )3
6 )
V I=1Me (RaX− X
3
6 )V I=
1Me (RaX− X
3
6+Me)
V I=1Me (Rc×(2L−X )−
(2 L−X )3
6 )
